Trivia: The machine is called "Sissy," which is short for "Sisyphus." In Greek mythology, Sisyphus was cursed to push a boulder uphill for eternity - every time he'd reach the top, it would roll back down and he'd have to start again. The use of the name "Sisyphus/Sissy" is a reference to the fact that Tree has to relive the same day over and over again, much like Sisyphus must push the rock up the hill over and over again.
Trivia: The costume designer threw in Easter-Eggs that most people never notice. When Tree wakes up in the other dimension, she's wearing the same clothes from the first movie, including a concert-tee. However, if you compare the shirts from the two movies, while the picture is the same, the words are slightly different. (Ex. A different venue is listed on the shirt.) This is to provide a subtle hint Tree is in another dimension. There are similar tiny changes in the other character's clothing, too.
Trivia: Just a funny bit of censorship to look for. In the film, Tree wears a shirt that says "FML" in one scene. For those who don't know, this is an abbreviation for the phrase "F**k my life," which is a phrase commonly used to express frustration when something bad happens. But because of its profane connotations, the shirt was digitally altered in trailers to instead say "OMG," which means the much less naughty "Oh my god."
Trivia: Spoilers. In the end, Dr. Butler and his wife Stephanie are revealed to be the killers. They were actually the killers in the original script for the first film, but the ending was changed several times until the final version seen in theaters with Lori being the killer. The original idea was recycled into this film, since the dimension-hopping angle of the story allowed the presence of a new version of the killer.